What question did this study set out to answer?

The goal is to count integer solutions to specific equations and congruences, assessing their error terms.

April 15, 2026Open Access

Distribution of integer points on determinant surfaces and a mod‐ p analogue

Key Points

The goal is to count integer solutions to specific equations and congruences, assessing their error terms.
Developed asymptotic formulas for integer solutions with smooth weights.
Analyzed integer solutions related to determinant surfaces.
Considered congruences involving large primes.
Established an explicit main term for integer solution counts.
Provided strong bounds on the error term based on variable sizes.
Counted integer solutions effectively in both determinant equations and congruences.

Abstract

Abstract We establish an asymptotic formula for counting integer solutions with smooth weights to an equation of the form , where is a non‐zero integer, with an explicit main term and a strong bound on the error term in terms of the size of the variables as well as of . We also establish an asymptotic formula for counting integer solutions with smooth weights to the congruence , where is a large prime, with a strong bound on the error term.

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Cite This Study

Ganguly et al. (Wed,) studied this question.

synapsesocial.com/papers/69df2b2ce4eeef8a2a6b0161 https://doi.org/https://doi.org/10.1112/mtk.70093

Discussion

Journals

Mathematika

Institutions

Indian Statistical Institute

Max Planck Institute for Mathematics

References and Citations

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